Scientists observe an approaching asteroid that is on a collision course with Earth. They devise a plan to launch a rocket that will collide with the asteroid inelastically and stop it.

The mass of the asteroid is 9000 kg, and it is approaching Earth at 45 m/s. If the rocket has a mass of 1800 kg, what velocity must it have to completely stop the asteroid after the collision?

A. -225 m/s
B. 306 m/s
C. 45 m/s
D. -116 m/s

To completely stop the asteroid after collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity:

momentum = mass * velocity

For the asteroid before collision:

momentum_asteroid = mass_asteroid * velocity_asteroid

For the rocket before collision:

momentum_rocket = mass_rocket * velocity_rocket

Since the rocket collides inelastically with the asteroid, they stick together after the collision. The final velocity of the combined system (rocket and asteroid) will be zero since they come to a complete stop. Therefore, the total momentum after the collision is zero:

momentum_after_collision = (mass_asteroid + mass_rocket) * 0

Using the principle of conservation of momentum, we can set the initial momentum equal to the final momentum:

momentum_asteroid + momentum_rocket = momentum_after_collision

mass_asteroid * velocity_asteroid + mass_rocket * velocity_rocket = 0

Substituting the given values:

9000 kg * 45 m/s + 1800 kg * velocity_rocket = 0

Simplifying the equation, we can solve for the velocity of the rocket (velocity_rocket):

velocity_rocket = - (9000 kg * 45 m/s) / 1800 kg

velocity_rocket = - 225 m/s

Therefore, the velocity of the rocket must be -225 m/s (negative indicating opposite direction) to completely stop the asteroid after the collision.

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